{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Chapter 6, demo 1\n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "\n",
    "Posterior predictive checking demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import preliz as pz\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# data\n",
    "data_path = os.path.abspath(\n",
    "    os.path.join(\n",
    "        os.path.pardir,\n",
    "        'utilities_and_data',\n",
    "        'light.txt'\n",
    "    )\n",
    ")\n",
    "y = np.loadtxt(data_path)\n",
    "# sufficient statistics\n",
    "n = len(y)\n",
    "s2 = np.var(y, ddof=1)  # Here ddof=1 is used to get the sample estimate.\n",
    "s = np.sqrt(s2)\n",
    "my = np.mean(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create 9 random replicate data sets from the posterior predictive density.\n",
    "# Each set has same number of virtual observations as the original data set.\n",
    "dist = pz.StudentT(nu=n-1, mu=my, sigma=np.sqrt(s2*(1+1/n)))\n",
    "\n",
    "replicates = dist.rvs(size=(9,n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RixYtVL9+fe3Zs0dvvPGG4bWS5vpIkp4JbG27krdu3VovvPCCAgMDFRcXp9OnT2v//v3atGmTPD3Tzs3j4+PVpEkTvfjii8qfP79WrlypqVOnGhpxI0eO1KOPPmoof/Jy+Pj4qHfv3mrcuLH8/f118OBBffnllzp79qykuw3xMWPGaNSoUS59jSlTpig6Otrwfho2bKhXXnlFBQoUsL6XzLJYLBo+fLjhh0L58uXVv39/hYaG6tatW1q1apWmTJli/dwWLFigNm3aGIZePPHEE3r22Wc1Z84cSXf3qSFDhmjw4MGaPXu2dT0vLy+NHj3a7o6dnp6eqlWrlpo0aaKQkBAFBQWpUKFCunnzpiIiIjR9+nRDEDpjxgz169dPvr6+qb63fPnyafjw4apdu7Y2b95sCNnu3Lmjbdu2qWjRonrvvfdUoUIFLVy4UD/88IN1nRs3bmjt2rV6+umnU/0c4+PjFR4ervDwcHl6emr+/PmaP3++4fkvvvgiXXV28+ZNDR8+3PBj5P7771evXr1Uvnx5Xbt2TfPnz9e8efOsz48fP14tW7bM9FVcR/7991/DY19f3xSHQySpUaOG3bJ//vkn1b+Ji4tT+fLlNXjwYJUuXVp79uzR559/bmho//jjj+ratau1t6ntd0f37t3Vpk0bFSxYUDdu3NDJkye1Z88ebdy40W4IpCuOV0cSEhJUo0YN9e/fX+XKldOlS5esYU7Hjh0NP+JWr16tjz76SHny5LEuW7ZsmeH1Wrdurbx580pyzXEbHx+vL7/80rANb29vDRgwQI0bN1Z0dLS+/fZb69X6zFi/fr3dj9rSpUtb53FzVMcpKVmypFq1aqUGDRqoSJEiCgwMlIeHhy5duqR169ZpxowZ1mDk1KlTWrVqlbWXwezZs5WQkKA33nhDe/bssb5mixYt9Pbbbxu2k/w8lpltuqPz589LuntRZe/evZo4caLh+QcffFC1a9e2+7sRI0YoMjLS+rho0aJ69dVXrcNo//rrL3399dfWC3YbN27UokWL7HosJpeQkCAfHx+9+uqratSokaKiouz2y5MnT+qnn35y+RC78ePH212kKFu2rHr16qX7779fnp6eOn78uFasWGEXcGbmnFarVi2tXbtW58+fV5cuXQyv++WXX+r++++3Pk7+neGKz3/UqFF2QdeLL76oVq1aKS4uTtOmTdO6devS9Tk6cuTIEbuhw4GBgXrnnXcUFhamf/75RyNHjjS8n5QEBQWpXbt2evjhh1WsWDEFBgbK19dX0dHR2rx5syZPnmx9z1evXtW8efPUq1cvSXc/z1u3bmnUqFGG7+T777/f7vuxaNGiLtmmlLPnrKQbM3Tu3NnQzu/WrZu6d+9u9/nGxMQYLlT4+vpq6NChqlu3rnx9fRUTE6Pjx49r586dqV6oAu4VhF1ABiT96E6ubt26hrlfPvjgA505c8aut5IzXn75ZfXt21eSVLlyZd26dcs6DE26O9wkIiJClStXlr+/v/z9/R32KEg+10d62V5h7Natm6FRFxoaqmbNmmnQoEFO/SgKCwvTxIkTrQ2F6tWrKy4uzjC/xbFjx7R//35Vr15d0t1GRHKvv/66Xn75ZevjihUrqkiRInrxxRety5YuXap3333XGuC44jWWLFlieI1y5cppypQp1nl9HL2XjNixY4cOHjxofezj46Pp06cbhqxWr15d586d02+//WZd9vPPP9vNMzJs2DDt2LHDGoocPXpU/fr1MzSc+/XrZxjqkaRp06Z2vV2ShIaGqkGDBnrwwQety27cuKFDhw4Z9g9HBg0aZG3IV6xYUQsXLrT2OEvywQcfWOfvGjx4sBYtWmS4Cnv48OE0w66mTZsajsXatWsrKirK0CPgf//7n6Kjo52eX2blypWGhn5gYKCmT58uPz8/67JatWrp+PHj2rFjh6S7x9DcuXP1zjvvOLWN9LANXwsVKuRwnqnkgoKC7JaldVXd19dXM2bMULFixSTdnV8kICDA0JMxISFBy5Ytsw5Dtv3u6NWrl4oUKWJ9XLVqVT355JN655137L47XHG8OnLfffdp5syZ1voqX7686tWrJ+lucF2iRAlrqHDjxg2tW7dOTz31lKS7w5xsfzSEh4db/98Vx+2mTZvsfkj269fPeh6Q7p5jHn/8cV26dCnF9+mM5GWQ7obeP/74o0qXLi3JcR2nxPa7MUnFihXVoEEDnThxwnDcbd261Ro8JQVYyQMC6e5FmdTOW5nZZnqcP39eCQkJdsuTDx++fPmyTp8+bbdOnjx5DD/GM8M2YEmucePGdiGAdLfstm2UCRMmGOaLCw0N1bVr1wzh2ezZs1MNu6S738vJjz9H++Vvv/3m0rDr9u3b+uWXXwzLSpcurXnz5qlQoULWZRUrVtQTTzxhN8Q7M+e0PHnypLg/FilSxOFzrvj8jx07Znd+DA8PN8zRWr9+fbVr1y5DPZWTs/1OkO7O15bUPqhSpYrKly/v1J1Hk1+gSq58+fKqU6eOLl++rFmzZlmXb9261Ro8JR0zthdmU6uDzG5TytlzVtL7sh02m/y55GzLWrp0aT3//POGEK5WrVrq0KGDEhMTHfZoBu4lhF1ABhw4cMCuEZx8zqPkyzISdr3wwguGxxUqVLBb58qVK+l+3fSoVq2aoey9evVS48aNVbFiRZUrV06VKlVShQoV5OHh4dQ8H+3bt7e7ItaxY0e7gGjPnj2qXr26Lly4oJMnTxqeGzVqVJo9OO7cuaNdu3apcePGLnmN06dP2/24bNeunV2w4Oi9pJftEL74+HhDTzdn/06S8ubNqy+++ELPPPOM9Ypm8n22Tp06hh/StiIjIzV//nz9/fffioiI0JUrV3Tz5s0Uh1OcP38+zbDLNqQKDg42NOYLFSqkJk2aWB97eXmpdOnShkDG9keMI8mDiCQdO3Y0/AC2WCzau3evHnvssTRfT7L/jKOjo1WrVq10/11wcLBTw1qygjPzrdh69NFHrUFXkqQ7PSYfzrl7927r/1erVk3Hjh2zPg4PD1fDhg1Vvnx5lS9fXiEhIdZgJfl3hyuO15T06NHDEEwm5+npqXbt2mnSpEnWZUuXLrWGXStXrjQMV0+aqDiJK47bvXv32j1vGzrkzZtXrVq10vTp09N87dTYbqtBgwbW+kjiqI4duXPnjlasWKE1a9boyJEjunDhguLi4lIcDpfSUPb0yK5tdu7cOc1hqSntn44mKne1l156SW+//bbDG0Q4muTbURvF1sGDB3Xjxo1UJ/a3/X51tF/+888/un79ulNtA2fs27fPbmjkyy+/bAi6knMUfGfFOS0lrvj8k/d2TGL72Xt4eKhDhw6GizsZYfudULZsWbsLYdWqVVNYWJgOHTqU5uv98ccfWrFihQ4ePKhz584pNjbWYXAsueY7IbPbzI3nrJQEBQWpZMmSOnfunKS7oWiHDh1Up04da3lDQ0MVGBgoT0/PdI3oAMyIsAvIAEdX1h1NGpuRO/Tly5fPbvL5pOEyyaU1t0ZmdevWTcuWLbOeyGNiYvTrr78a1gkICFDLli3Vr1+/NK9iO7pC5WhZUu+GzDSAkuZDcMVrREVF2T3n7HtJr4yW9/Lly0pISLC7MhgaGqo33njD7g6cfn5+GjNmTIo9gdatW6c333wzXfOupLVugQIFFBAQYFhmu1+XLFnSrky26ziz36d3X3NGRusmPdtIj8DAQOuwCOlu+H3nzp1Ue3c56sWV1l2aHH1unp6euu+++wxBSPLvxP79++t///ufdXvnz583DCOVpOLFi+vpp59Wr169VKBAAUmuOV5TUrVq1VSf79ixoyZPnmz94bthwwZdvXpVBQsWtJvDyzaEcsVxa3tO8fX1tQsZJdd8z9huy9k6thUdHa1XXnnFrvdJam7cuOH0urllm7nVDz/8oBMnTmjcuHF2x31G90mLxaKoqKgUw65ChQpZj9fkbPchi8Wi6Ohol4Vdjo7vatWqOf33WXFOS40rPn9H7cysans4852QtDy1sCsuLk4DBgxIcy7I5DJ7fLpim7nxnJWaIUOG6I033rC2hw4ePGjoXSzdbf89//zz6tSpk1NTjQBmxd4PZICjK4GOrq5mhKMfnzlxogoMDNSiRYv02muvKTQ01OH7i4mJ0ezZs/XMM8+k2ePG2c/HFZ/jrVu3XPYaWVnXrmKxWFJ8z47m+ImLi9P+/fsdrh8dHa3Bgwenu6GfVq8hR1fabffr1IahpUd27mtpyaohBLZ3O7t9+3aaPcYc9R6qXLlyqn+T0mdkW9/J1ytXrpyWLFmiV155ReXKlXP49xcuXNCUKVPUvXv3FK++p0dax7yj4Ci50qVLW4c1Snc/z6Shq7bzsbjqjojJj1tne91lpHdeWq/hbB3b+uSTT9IVOrlCTmwzp61du1b79+/X4sWLVb9+fbvnbOfwyqzUvrPSs6+48vs1M/t9Vp3Tskp6P//c9J0wceLEdIVOruCKbebGc1ZqnnzySc2fP1/t27c3DLdM7vDhw3r//fcz3esPcHf07AIywFEvpjNnzthNEmvbvdnd5M+fX/369VO/fv2sE7mePHlSBw4c0KxZs6xzF5w7d06LFi1yOJlmklOnTtktczTXSdKJ29GP048++kiPPPJImuVO6kHkitdwNM+Rs+8lvWzLW6BAAS1atMipHw2OuqrPmTMnxbsnvffee6pZs6Zh4mfp7h0Hba96Pvvss2rbtq2KFi0qLy8v3b592zrEKzc6deqU3WTtqe1rzrCtm4oVK2rKlClp/l1a82hl1COPPGI3RHrRokUp9mBKTEzU4sWL7ZY3bNgw1e042tcTExOtQyiS2B4nRYsW1VtvvaW33npL169ft3537N69W7Nnz7ZOIH3gwAH98ccfatasmUuO15Q4c8EgPDzcEGwtWbJEsbGxht6EzZo1s7sg4Yrj1nZfvH37ti5evGjXy9eZuz2mpUiRIoZegc7WsW35bL9bqlSpogEDBqh8+fLWIaMjRoxw2d3zsnubKU38PW7cOOvd+j777DOn5jHKLB8fH4WFhWnSpElq3bq1of6mTp2q8PBwlSxZ0rrMdp/08PDQokWLHPbKsmW7zyUXExNj7fGYnO1+6eHhkWav0fRwVKYDBw4Y5sBKSU6c01zx+afU9rB9bVd9JyS/y6ej7wRntmXbC/a+++7T66+/ripVqlh7C06dOtVu/rXMcNU2c9s5Ky1Vq1a19tq/dOmSTpw4oYiICP3555+G78nZs2drwIABmd4e4K7o2QVkQLVq1eyGjNneyUaS4c5sWc3Hx8duWWauHEVGRhqu4uXNm1ehoaFq3ry5Xn/9dbsGfvL5DhxZuHCh3VVB227ikqyN1xIlStjNI7NmzRrdd999Cg4OdvjPz89PBw4csA6dcMVrlC5d2q7RuXjxYrvhdI7eS3rZXrW/du2a9uzZk2JZg4ODdenSJV29etXuh/WxY8f02WefGZaVKlXK+v8xMTF666237G4hb9stP3/+/Proo49Ut25dlS1bVsHBwYY7AeVGjurCdpmHh4fDuxOmxLZujh8/rosXL6ZYL6VKldKJEyfsrgCfPn1aVapUMfxL7XbvKenQoYPdD6eff/5Z27dvd7j+pEmT7Hp+1a9fX6GhoaluZ8OGDXbDLdasWWM3vC353DaO9qHq1aurZcuWGjZsmN18Vkm3fHfF8ZoZTz75pOF1tm3bZrh7qeR4PjhXHLeO5gay3Wdv3rxpd1fIjLANCLZs2WL349ZRHSd3+fJluzveDRw4UM2bN1flypUVHBysQoUK2Q2tccT23JVSzxZXbtNd+fv7a9CgQYZlN2/etOvdZbtPWiwWbdiwIdV9Mi4uTufOnXPYlkhuwYIFdtu33S8rVarksiGM0t07ydpe0Pnhhx907do1h+sn72nuqnOao88lpX3VFZ+/o+8E28/eYrFo4cKFaZY9LbbfCSdOnLA7lxw4cCDN+bpszxXdu3dX27ZtVaVKFQUHB6t48eIOexjbcvY7wVXbzA3nrPS8Z9vyFilSRHXq1FF4eLjGjh1raBvcuXNHERER1seuaoMA7oKeXbinpNX7plixYvL19U3zdfz9/dWsWTOtWLHCumzjxo0aOnSonnnmGeXLl09z5szJ0OT0GeXornLTp09X165drVe8ixYtanfnq5T88MMPWrlypZo0aaJatWqpbNmyKliwoOLj43XgwAG7xm1qE9pKd7tU9+3bVz169JC/v79WrlxpuDuOdHci/uQBRJcuXQzzTW3YsEE9evRQly5dVK5cOXl5eenSpUs6fPiwNm7cqM2bN6t27dpq0aKFS1+jTZs2mjZtmvVxRESEevXqpZ49eyp//vwO30tG1KlTR6GhoYY7Kw0bNkwHDhxQkyZNVKxYMd28eVOnT5/Wnj17tG7dOv3777/67LPPDD16bt++rTfeeENxcXHWZU899ZTefvtttWnTxtojb+vWrZo8ebJhonrb/ej69ev66quv1LJlS925c0cbN240TOSdG61fv17Dhg1Tx44d5eHhoQULFtj19GjYsKHDK+cpad68uUaPHm2dg8tisah3797q3r27HnroIQUFBSk2NlYRERHavXu31qxZozNnzmjGjBl2jWFXKFiwoN544w19+OGH1mXx8fF66aWX1L17dz3++OMKCAjQmTNnNH/+fC1fvtzw93ny5NGQIUPS3M7t27fVrVs3DR48WKVLl9aePXv0+eefG9bx9vY23O3uk08+0b///qvGjRvr/vvvV+nSpZU/f37dvHlT27dv1+bNmw1/n/xHrCuO14xKmmh7zpw5ku72bkr+I6FkyZIOr9i74rh96KGHVKRIEcPcORMmTJCnp6cee+wxRUVF6dtvv830nRglqW3btoZz1507d6yTnZcpU8ZhHdsqVKiQvL29DWHuDz/8oIIFC6pIkSI6duyYJk6c6NScNrY9gDZv3qyNGzeqbNmy8vDwsN7Z0JXbdGetW7fWuHHjDAHlwoUL1a9fP2tP3ZIlS6pJkyaG772vv/5ap06dUsuWLVWiRAklJCTo3Llz2rdvn9avX6/9+/drwIABhuG8jnzxxRdKSEhQw4YNU9wv27Zt68J3fHcOu2effVY//vijddnJkyfVsWNH9e7dWzVr1pSHh4dOnjypVatW6caNGxo7dqwk153TAgIC5OnpabhA9Msvv6h48eLW4KJw4cLy9/d3yedfqVIlVa1a1RDeLliwQAUKFFDr1q0VFxenH3/8MdN3YpTu1tf3339vWDZw4EANGTJEoaGh1u+rtBQuXNgQPs2dO1cVKlRQcHCwTp8+re+++86pMNq2zg4dOqSVK1cqNDRUXl5e8vb2tu7rrthmbjhnFS5c2HC+WbNmjZo0aaLixYvLw8ND+fLls34u7dq1U8WKFdWwYUOFhYWpRIkS8vPzU0xMjJYtW2YXAjNJPe5lhF24pzz++OOpPr948WKFhYU59VqDBg3SH3/8Ybj6snDhQsNVtrx582bbbX/LlCmjwMBARUdHW5fNmTPH+sNNkmbMmKEGDRo4/ZpnzpzRrFmznApy0rqrjJ+fn9avX5/q8JJ33nnH8LhLly5au3at4a5lf//9t/7+++80y+PK1+jVq5d+/fVXwwTfGzduNMwTYfsjLCM8PDz0ySefqGvXrtb5RW7duqUffvghxVtrOzJq1ChDA7ho0aL64IMPFBAQoPfee8/wOX/77bd6+OGHrVeRGzduLF9fX8Pd5yZNmmT4MVC0aNFcPemzn5+fFixYYHcVPImPj4/efPPNdL/mxx9/rP79+1t79V29elXjxo3TuHHjMl3mjOjcubNOnDhhCGJv3bqlKVOmpDrE0sfHR6NGjXJqgmdvb2/9999/6t+/f4rrdO/e3W447LFjx9Ls7Zn0+smHUrrieM2Mjh07Gr4zk2vfvr3D4ZCuOG59fX01aNAgvfvuu9ZlCQkJ+vrrr/X1119bl7nie6Zp06aqV6+e4TM+efKkBgwYYFgvtW3lzZtXjRo1Mnyf79y5U926dTOsV7Ro0TRv0lC7dm3DUKSYmBi9/PLL1sdJdzZ05TbdmZeXl15++WV98MEH1mXx8fGaMmWK/u///s+67N1339W+ffusQVRiYqLmzZuXqR7nvr6+unPnjsaMGaMxY8Y4XCc4OFhdunTJ8DZSMmDAAP3111+GXlgREREaOnSo3brJ23quOqflyZNHYWFhhjnj1q1bZxjumnxYqys+/7fffls9evQw9IqfNm2a4TvfFd8JoaGhatu2rX777TfrsujoaL399tuG9dLaVvPmzQ3txWPHjqlnz56GdZw5Pm3vdBwfH69XX33V+rhUqVLWz91V28zpc1bt2rUNc6xGREQYjqP27dtbQ7XExERt27bN4Z24bQUHB9vN8QncSxjGCGRQ+fLl9dVXX6XYEywgIMDhlTBneo5lhKenp3r37p0lr52W3r1768EHH0x1nQ8++CDVHi6DBw/WY489Zljm6+urSZMmqWXLlk6XxfZHtyteIygoSOPHj09xWIaPj0+aPSGcVb16df34449O32HJ19fXcBX0jz/+sLvl/SeffGKdr6Fdu3aGK4oJCQl68803rb29ihcvrqFDh6Y431BAQIDLJ0R2tdGjR6c4X4y3t7c+++wzp0Pt5Jo0aaLx48c7PReNv7+/yybdT8nQoUM1cuRIhz07HalcubJmz56tJ5980qn1u3btqgceeCDF5x9//HG7YVXO8vLy0vDhww0TArvieM2MmjVrKiQkxG65h4dHqnMzZfa4laRnnnlGPXr0SPFvypUrp4EDBzr1+qnx8PDQV199leoPoBdeeCHVepek4cOHp3oX3r59+6Y5J5wkPf3007rvvvvSXM+V23R34eHhdp/DvHnzDL3agoODNXPmTKe/67y8vNK8q3LRokU1YsQIu2kckgQFBWnixIlp9vTOiPz582vatGlq1KhRuv7Olee0Pn36OL1dV3z+Dz30UKplL1KkiIYNG+Z0mVLzwQcfpNqrr1mzZmnOazZw4MBUv1fatWunTp06pVmWRo0aOX23TVdt0xlZec7q0qWLS4f+Snf37S+++IK7MeKeRs8uIBOaNm2qxYsXa+LEifr7778VExOjYsWKqVGjRurXr5/++ecfu79Jz9Cp9HrxxRcVGBioOXPm6MiRI7p+/XqG79TTq1cv1a5dWzt37tS+ffsUGRmpqKgoxcXFyc/PT6VKlVKtWrUUHh7ucG4JWyVLltTixYs1depUrVy5UmfPnpWfn5/uv/9+vfzyyyn2OMufP7+++uor9ejRQ4sWLdLOnTt19uxZ3bhxwzq8pWLFiqpbt64ee+wxVaxYMUteo06dOlqyZIkmTpyoDRs2KCoqSgEBAapXr5569+6t0NDQdPcWSkmtWrX0+++/a/ny5Vq7dq0OHDig6OhoxcfHK3/+/CpVqpTCwsL04IMP6rHHHrPOzxAZGWl3lfvZZ5+163X34YcfaufOndYrnadOndKHH36o0aNHS7rbY6h8+fL64YcftHv3bsXFxVn36759+7o0XMgKYWFhWrp0qSZNmqT169frwoULKlCggOrXr68+ffpkKOhK0qRJE61Zs0a//vqrNmzYoEOHDikmJkaJiYkqUKCAypQpo2rVqumhhx5So0aNlDdvXhe+M8fat2+vp556SkuWLNGmTZus+0tcXJzy58+vYsWKqXbt2mratKkaN26crruk+fv7a+bMmZo9e7Z+/fVX61wllSpVUqdOnaxDRZMbPny4nnjiCe3cuVMHDx7UpUuXFB0drdu3b8vf31/BwcGqV6+eOnXqlGXHa2aEh4fbXaho0KBBmsNRM3rcJjdkyBA1aNBA06dP1/79+xUfH69SpUqpRYsW6tmzp2H4YWYULVpU8+fP1/fff6/ly5fr1KlT8vPzU1hYmF544QU98cQT6tq1a6qvUbp0aev5b/369bp48aLy58+vatWqqVu3bmrcuLFTQ2ULFCigX375RePHj9dff/2lCxcu2M3N5eptujtfX1+9+OKL1u9s6e6Q4++++07Dhw+3LqtQoYIWLFigdevWacWKFdZz+a1bt6zD7apUqaL69euradOmTrVPOnTooCpVqmjq1Knatm2brly5omLFiqlp06bq27dvlrZxgoKC9N1332nbtm367bfftHv3bp07d05xcXEqVKiQihcvrjp16tiF+a46pzVv3lxTpkzRjBkztH//fl29etVu3svkXPH5d+/eXdWrV9fUqVO1a9cuxcbGqkSJEnrsscfUt29fh+3MjPD399e0adP0008/afHixTp+/Li8vb1VuXJlhYeHq2PHjg570SUXEBCgOXPmaOrUqVqxYoXOnDkjPz8/Va5cWc8++6yefvppp3pCe3t7a9q0adbj/MyZM4aeea7eZm44ZwUHB2vu3LmaMGGCtm3bZj13ODJr1ixt375dO3bs0PHjxxUVFaXo6GhZLBYVKlRIFSpU0COPPKJnn33WpTeKANyRhyWn7q0L3AOGDx9umGQ4KChIf/31l0tvyZ0bnT592m7IaHqHUALO2LJli90wprVr1zrdwwYA4FjyO09KxuFjAADkdvTsAjLh448/VuHChdWsWTNVrlxZXl5eku7eHebnn3+2u5tWhw4dTB90AQAAAACQkwi7gEw4d+6cZs2apXHjxsnHx0eFChVSfHy8rly5Yrdu5cqV0zXfAwAAAAAASD9mrANcJD4+XpcuXXIYdDVs2FA//vijyyefBAAAAAAARvTsAjKhf//+CgsL0/bt23XmzBnDhJalSpVSzZo11bp1a9WtWzeniwoAAAAAwD2BCeoBAAAAAABgGgxjBAAAAAAAgGkQdgEAAAAAAMA0CLsAAAAAAABgGoRdAAC4uSpVqhj+LVy4MN2vcfr0abvX2bJli8vKOGTIEMNrd+3a1WWvfa/L6rrLCq7YZ92JO9bRvSY7v6Putf0fAHICd2MEkCOOHz+uZcuWaceOHYqIiNCVK1cUHx+v/Pnzq1y5crr//vvVtGlT1a9fXx4eHjldXNxjtmzZoq1bt1ofFyhQQC+++GLOFQjI5dasWaNDhw5ZH5cqVUodOnTIwRIBGDdunOFxs2bNFBYWlmXbu3jxojZt2qTNmzfr6NGjunDhgq5evSp/f3+VL19ejRs3VufOnVWoUKEsKwMAJCHsApCtIiMj9eGHH2rNmjVydDPYy5cv6/Lly9q1a5emTZumFi1aaOzYsTlQUtzLtm7dqm+//db6uFSpUoRdQCrWrFmjRYsWWR/Xr1+fsAvIYcnPY9Ldc1lWhl1vvvmm4UJRkpiYGO3atUu7du3SzJkz9f3332dpOQBAIuwCkI327dun3r17Kyoqyum/uXz5chaWCECSEiVKaO3atYZlRYsWzaHSID2oOwDuIioqSoMGDdLy5cvl5eWV08UBYGKEXQCyxZkzZxwGXcWKFVPXrl1Vr149FS5cWNevX9fRo0f1559/2v14A5B1vL29FRwcnNPFQAZQdwByi3z58qlNmzZ67LHHVLZsWV2+fFnffvutNm/ebF0nIiJCe/fuVe3atXOwpADMjrALQLb4/PPP7YKuevXqaeLEiSpQoIBhefXq1dWhQwedO3dOq1atMjwXFRWl1atX6+DBgzpy5IiioqIUExOjuLg4+fn5qWTJkqpevbratm2rhx56yGFZxo0bZzdEbd26ddq7d69+/PFHbdu2TTExMQoKCtKjjz6qAQMGqHjx4ul6v+PHjzcMvyxTpoxWrVrlcP6x3r17648//rA+bt26tb744gvDOnFxcVq0aJH++OMPHTp0SDExMfLy8lJgYKCqV6+uJ598Ui1atHB4lTSl95vc6dOn9fjjjxuWzZgxQw0aNEjX+7ZYLFq9erWWLl2qQ4cOKTIyUvHx8SpUqJACAwNVrlw51axZU3Xq1FGdOnUMf1ulShXD488++0ytWrXStGnTtGzZMp08eVLe3t6qWrWqunXrpmbNmqValoMHD2revHnasWOHzp07p9jYWOXPn19lypTRgw8+qOeee06lSpUy/M2QIUMMQ7GSnDlzxmH5nBmmtWXLFnXr1s36OE+ePNq+fbt8fX2ty9566y399ttv1sezZs1SvXr1rI/nzZund9991/q4XLlyWrlyZarbjY+P188//6zFixfrv//+k3T3M+7cubPatm1rt3569gGLxaINGzZo+fLl2rt3ryIjI3Xz5k0FBASoZMmSql+/vtq0aaPQ0NBUyyhJ27dv17Rp07Rz505dvXpVJUqUULNmzdSvXz8VLFgwzb9PTUREhObMmaOtW7fq9OnTun79uvz9/XXfffepbt26evbZZ1W5cmWHf9u1a1fDcJz27dtr5MiRWr58uebMmaNDhw4pLi5OpUuXVqtWrfTKK68oT548KZYlKipKc+bM0aZNm3Ts2DFdu3ZNfn5+Cg4O1sMPP6yuXbuqRIkSGXqfztbdvn37NG/ePO3atUtnzpzRzZs3lT9/fhUuXFilSpVSjRo1VKNGDT322GPy9nauiWj7OSXZunWr3TGT1ndKevfZ5I4ePaq5c+dq+/btOnv2rGJjY1WgQAFVqlRJjz/+uDp16qR8+fI59Z5SYrFYtH79ei1btkx79+7VpUuXFB8fr4CAAIWEhOjRRx9Vx44dlT9/fqdf8/r165o6dapWrVqlM2fOyM/PT7Vr19ZLL72k+vXrO/ybCxcuaPbs2dq8ebNOnDihGzduyMfHR4ULF1axYsVUrVo11ahRQ40bN1bhwoXt/v7OnTtauXKlVq5cqX379ik6OlqJiYkqUqSIateurfbt26thw4YOt53S+WTTpk2aMWOG9uzZo5iYGD399NO6du2a1qxZY103pWkJLBaLHn/8cZ05c8a6bODAgRowYIBhvcweQ3fu3NHs2bO1aNEiHT9+XD4+PgoNDVWXLl305JNPpvh3GXH+/HlNmDBBGzZs0KVLlxQYGKhHHnlEffv2VZkyZdL8+xs3bmjFihU6ePCgDh8+rMjISF25ckXXr19X3rx5VaRIEVWtWlUtW7ZUs2bNDG0LR98HSYYOHaqhQ4daHydvD2Rmm0natm2rb775RoGBgYblY8aM0SOPPGJYdubMGcIuAFmKsAtAljtx4oTdD/OAgACNHTvWLuhKrmTJkurevbth2a5du/T+++87XP/atWu6du2ajh49qoULF6ply5YaPXq0Uz/apk6dqi+//FKJiYnWZefPn9fcuXP1xx9/aP78+ekKvJ577jlNmjRJt2/fliSdPHlSmzdv1sMPP2xY7+rVq/rrr78Myzp27Gh4vH37dr3xxhu6cOGC3XbOnDmjM2fOaOXKlapataq+/vprlS1b1ulyupLFYtFrr73mMISJiopSVFSU/vnnH61evVrly5fXihUrUn29S5cuKTw8XP/8849h+ZYtW7RlyxZ17drVEAAluXXrlkaMGKG5c+faPRcTE6OYmBjt3btXP/zwgwYNGqSePXum852mT+3atZU3b17dvHnTWr79+/frgQcesK6zY8cOw99s27bNEHZt27bN8HxaIeTly5f17LPP6sCBA4blSXOmnDhxQgMHDszQ+zl16pQGDx6s3bt32z0XGRmpyMhI7d27V7dv39bw4cNTfa2xY8dqwoQJhvn7Tp06pR9//FEbN27UnDlz5O/vn+4yJiYmauzYsZo8ebLhmJakK1eu6MqVKzp06JBmzZql7t2766233krze+L27dt69dVX7fbvY8eOaezYsdq6dat++OEHh4Hz/PnzNWLECMXFxRmWx8fH6+DBgzp48KBmzJih//u//9MzzzyT7vfrjJkzZ+qTTz6xmysx6fOIiIiwfhdt3Lgx24dBZnSfvX37tkaNGqWZM2faPRcdHa2tW7da62bcuHG6//77M1S+8+fPa9CgQdq1a5fdc0n7/V9//aVJkyZp9OjRatSoUZqvee7cOQ0fPlynTp2yLrt165bWr1+vP/74Q2+//bZeeuklw9/s3LlTPXv21PXr1w3L4+PjFRsbqzNnzljL+OWXX6pVq1aG9Y4fP65BgwbpyJEjduVJOp8sXbpUTzzxhEaOHOlUcDdhwgR98803dsvDw8MNYdcff/yha9eu2Z33d+7caQi6PD097S4kZPYYio2NVZ8+fQx3wIyLi7PuH506dXI4j2hG7Nq1Sz179tS1a9esyy5cuKCFCxdqxYoVTs1DevLkSQ0bNszhc9evX9f169cVERGh5cuXq379+po4cWK6Qtas2mZK319J57/kMnsxAwDS4pnTBQBgfsl7LSXp1KmT3ZU/V1u+fLnd5KyOnD17VmPGjLH7UZzk4sWLGjNmTLq2HRQUpJYtWxqWOQpf1qxZo/j4eOvjUqVK6cEHH7Q+3rt3r15++WWHQZetgwcPqnv37oqMjExXWV1l1apVafY2So+xY8faBV3JzZw5Uz///LPd8rfeesvhZ20rISFBY8aM0aRJkzJVzrT4+vraXb3evn279f/PnTtn+KEn2YdfydeXZNhHHPnqq6/sQoPkJkyYYO05kx4XLlxQ165dHQZd6bVr1y6NHz8+xR+Y//zzj6ZOnZqh1x49erQmTpyY4jGdxGKxaNq0afrwww/TfM3ly5enun///fffWrhwod3yOXPmaPjw4XY/0m3dvn1b7777rhYvXpxmWdIrMjJSn3/+uct+zGeFjO6zQ4cOdRh02bpw4YJ69Oihf//9N91li4mJUffu3R0GXbYuX76svn37GkKVlHzwwQeGoCs5i8Wizz//XBs2bDAsf//99+2CLmedPXtW3bp1cxh02Vq9erVee+013blzJ9X1zp8/7zDokqTGjRsbQtNbt27Z9daWpKVLlxoeP/zww7rvvvusj11xDH300Uep1sncuXNdcv6Kjo5Wv379DEFXcrGxsRm+0JCSrVu3OvUdllPbTExM1MiRIw3L8uXLZ9e7GwBcjZ5dALJc8tvRJ0lpiGFaPD09VatWLTVp0kQhISEKCgpSoUKFdPPmTUVERGj69OnauXOndf0ZM2aoX79+hiFjtiwWi7y8vDRw4EA1a9ZMp0+f1vvvv28ImFauXKlPP/1UPj4+Tpe1W7duhkb3mjVrFB0dbQj5li9fbvibDh06WIcGWCwWvfvuu4Yrop6enurVq5cef/xx3b59W3PmzDEMfzt37py++OILu4ZldrDtfdSwYUP17t1bxYoV0+3bt3Xu3DkdPHhQmzdvVnR0dJqvFx8fr9q1a6t///4qUqSI/vrrL3399deGcPDrr79W+/btlTdvXknSihUr7H6wVK5cWYMGDVLp0qV16NAhff7554btjxs3Tk899ZTKli2rt99+WwMGDND06dM1Y8YM6zrFixfX7NmzDa/raHhQSh588EHDfCXJwyzbz02629Phzp078vLysgvDPDw80gy74uPjVa1aNQ0ePFiBgYGaO3eufvrpJ+vziYmJWr58ufr37+/0e5CkTz75ROfOnTMsq1atml555RVVqVJFiYmJOnLkiJYsWeJwiIttGfPly6fBgwfrwQcf1MGDB/XBBx8YfsgvXbpUgwYNSlcZ9+3bpx9++MGwrESJEnrrrbcUEhKi//77T6NHjzaEDHPnzlXr1q1T7TFnsVgUFBSkIUOGqGrVqtqyZYs+++wzw/64dOlSQ8+Gixcv6tNPPzW8TqNGjdStWzcFBwfr0qVLmj59uqH3y4gRI9SkSRMVKlQoXe87Nbt27bIL1YcNG6by5ctLutuL8ujRo9q2bZv+97//peu1v/zyS926dUujRo0yHHv333+/vvzyS8O6qfUWy8g+u2bNGrugpGvXrmrZsqUCAgJ0/PhxffPNNzp69Kiku8O03n//fcPrOmPs2LGKiIgwLHviiSfUpUsXFSxYUH/++afGjx+vhIQE63t57733tHz58lR7DMbFxalJkyZ68cUXlT9/fq1cuVJTp041hJIjR47Uo48+Kulu6Jb0XqS7QfrQoUNVt25d+fr6KiYmRsePH9fOnTv1559/2m1vxIgRhoshRYsW1auvvqqaNWtKkvU7NqlH8saNG7Vo0SK73sbJJYVhrVu31vPPP6/ChQvr5MmTun79ury8vNSuXTtDaL106VKFh4dbHyckJNj18k3+vCuOoSNHjtgNTw8MDNQ777yjsLAw/fPPPxo5cqRLLhRNmTLF7vzWsGFDvfLKKypQoIC1jtPi4eGh0NBQPfbYY6pRo4YCAwNVuHBh3b59W2fOnNHcuXO1fv166/pLly7V4MGDVbx4ccMNK2yHM7799ttq0aKF9XHy/TMz20zJ7du3NXToUK1evdqwfPDgwRnqtQsA6UHYBSDLOQo20jsHVpKmTZuqadOmDp8LDQ1VgwYNDEHAjRs3dOjQoTSHrrz88svq27evpLvhyK1bt/Taa69Zn79165YiIiJSnN/HkWrVqumBBx6whm/x8fFauHChXnnlFUl3f7j8/fff1vVth27s2LHD7gp87969DT/+69atq8uXLxt+oC5ZskTvvvtupoc0pFfSD70k4eHhhjlnQkJC1LhxY/Xt29epnglFihTRtGnTrEFWWFiYvLy8DEFeTEyM/vzzT2vj3banV/78+TVr1iwFBARIujv/T7ly5fTss88ayj137ly99dZbCgwMVGBgoN3wisxOAG4bTu3cuVOJiYny9PQ09NoqWrSoIiMjFRsbq4MHD6pGjRp28yFVrlw5zV6R+fLl0/fff28N5P7v//5PW7duNfSUc6Z3R3IXLlywCxJr1aqlmTNnGsLkypUrq3Xr1rp69Wqar/nOO+/oueeekyRVrFhRFy9e1KhRo6zPnzp1SrGxsemaa8l2H/D09NS0adOswU5ISIhq1Kih5s2bGwKgn3/+Oc3hoZ9//rl1eFqlSpV07NgxQ3Bi+5nOnz/fEFaHhIRoypQp8vS827G+QoUKqlOnjp544glroHnt2jUtWbJEL7zwgtPvOS22x2ajRo0Mc95VrFhRDRo0UNeuXXXz5k2n5+uS/l+AZVtHefLkSdcxk5F9dtasWYbHXbp0MQxtrlChgkJCQvTEE09Yl23fvl1Hjx5VSEiIU+W6ffu2XY+9unXrGnoNV6tWTd7e3oa5Fk+cOKG//vpLjRs3TvG1w8LCNHHiRGswXL16dcXFxRl6qh07dkz79+9X9erV7XpZlS5dWs8//7whWK5Vq5Y6dOigxMREw753/vx5u5u+TJgwwRp0SXfPodeuXdPEiROty2bPnp1q2CXdnYsr+XuvWLGi9f/Dw8MN4c6WLVsUGRlp3W82bdpkaCMEBAQY9k1XHEPJLwglGTdunOrWrSvp7nmhfPnyTs3BmJYlS5YYHpcrV05TpkyxDm92VMeOhIaG6tdff3X4XJUqVdS4cWM1aNDA2oMsMTFRO3bsUMuWLVM9XxUuXDjF5zKzTUdu376tgQMH2vXuf+mll9SlSxeHfwMArkTYBSDLuXroTGRkpObPn6+///5bERERunLlim7evJnids6fP59m2GX7w7JChQp261y5ciXdZe3atauhp9m8efOsYdfq1asNP7Zth244mvQ5eUiTfFnysCshIUG7du1yas4YV6pWrZrh8fDhw7Vq1SpVqlRJ5cuXV8WKFVW5cmV5eXk5FcS1atXKGnQl6dixo12vtd27d6tFixa6c+eO3fC/Fi1aWIOuJLVq1VKVKlUMP5xthwm6Wo0aNZQ/f35ryHf16lUdPXpUoaGh1jJ7e3vrhRde0FdffWUtU40aNdI9hFG6+9nZ9jyrUKGCIThwJoxKztEQoP79+6fYazKt+Vjy5ctn9+PS0XF39erVdIVdtj3l6tevbw26ktx3331q1KiR4UYNae0D5cqVszumbMtr+5naluXo0aMKCwtL/Q38/3/nyrCrWrVq8vDwsH5Hzp07V6dPn1ZYWJjKlSunChUqKCwsTH5+fnbHXHZJ7z7r6Hj/6aefnOq1tW3bNqfDrr1799oNn3M0L9Gzzz5rd2OR7du3pxp2tW/f3q4HZMeOHe2CkD179qh69eoKCgpSyZIlrb0rjx07pg4dOqhOnToqX768ypcvr9DQUAUGBsrT09Nw3Dg6nzgzP9zBgwd148aNVHvh9OvXL8Xnypcvb7joc+fOHS1fvtw6H6dtz7w2bdoYvlNccQzt3bvX8FzZsmWtQVeSatWqKSwszGFPdGedPn1aly5dMixr166d3Tx+jurYkWvXrmnBggXauHGjjh8/rsuXLysuLi7Vtk5muXKbn332mV3Q9frrr6tPnz6ZLicAOIOwC0CWCwoKslt24cIFw9VfZ61bt05vvvmmYmNjnf6btNbNly+fXU8zRz/40pq7xJHmzZsbfpxERERoy5YtatCggX7//XfDusmHbkh3h28k5+Pj4/BOU6VLl7ZbZvu32eHpp5/W3LlzrT8sYmNj7d6jv7+/9U575cqVS/X1HF19LlCggAoVKmQIHpN+XMTExBjCQ0kp3vWqdOnShrArqz8vLy8v1a1b19Dw37Fjh4oVK6Zjx45JkqpWrapGjRpZw65t27apR48edj/2nAm7HIVGtncKTO/+7Ogzql69erpeI7ng4GC7oMzRcWfbKykttuVMbR9I7tKlS9aho47YBmZS2p+pM3PtOeLqeffKli2rF154wfoDOzExURs3btTGjRut6/j4+KhevXrq2bOn3Y00skN699mYmBjrcLv0Ss/n62i/d7RPFSpUSAULFjQEcml9rzj6jnO0LHl5hwwZojfeeMP6WSRNzp5caGionn/+eXXq1MnaAyqj+6LFYlFUVFSKYZePj0+awWF4eLjhos/SpUvVvXt33bx50zD8ULK/QYsrjiHbACqlnk3BwcGZCrts7zid0rac6fG4Z88e9enTx6kh/0nS0y7K6m1GR0drzpw5hmUvv/wyQReAbMUE9QCyXGhoqN2y5PMXOSs6OlqDBw9Od4MurZ5ljuZeSvqBkFne3t56/vnnDcvmzp2r6OhoQ08Z26EbjqQ1B5KzHIUcly9fzvTr+vr66qefftKwYcN0//33OxwKdePGDf3666965plnUpyYOUlK79e2Pl31uWQ125Bq+/bt2rlzp/X91K1bV2FhYdZebzt27NClS5cMk3J7eXkZhoamxLY3W9LfZoare2g6KqOrjruskBWfaUoc3bkss959912NHz9ejRs3dthTLj4+Xps2bdJLL73k0htNOCs7P99bt25lyeuml7PfXcnXe/LJJzV//ny1b99eRYoUcbj+4cOH9f7779vNdZVRqe2PQUFBaR63Tz31lGGf27t3r06cOKH169frxo0b1uXVqlVz2F7IiORldvackdnvOEd/n5HzU3x8vAYNGpSu0Cml7efUNiMiIuzaGm3bts1w+QAgI+jZBSDLNWnSRJ999plh2bx58/TSSy+la5LvP//809Awlu4OHWnbtq2KFi0qLy8v3b59W0899ZRLyu0qnTp10vjx460/sFatWqXKlSsbeqzYDt2QpGLFihke3759W+fPn1fJkiUNyx2FRskngrb9wejoh4vt5MsZ5evrq+7du6t79+66ffu2Tp48qZMnT+rw4cOaPXu29Wr71atXNXPmzBRvcy45fl/Xrl2zGyqW1HMwICBAPj4+ht5dJ0+edOq1U5s421UchV3JexTWqVNHnp6eql27tv73v/8pJiZGv/zyi+FvqlatqgIFCmR5WR1xNM/e/v37rZNn5xbFihUz1Luz+0BQUJDLw5XkPfck6ZFHHtFHH32U5t+ldkONzGjWrJmaNWumxMREnTlzRqdOndKxY8e0aNEi650QLRaLJk6caJjEOjdydLz369fProesI+k5hmy/h6W7+9QDDzxgWHblyhW776a0vlccfcedPn3abpltqFW1alXrcO5Lly7pxIkTioiI0J9//mkIKmfPnq0BAwYoICDA7n14eHho0aJFTn0Wqc2x6cwx4+/vr6eeekoLFiywLluyZIldLypHc4O54hgqUqSI4aJBShdabO+Km16OerE7W8fJ7dq1S2fPnjUsa968uTp37qwSJUpYb5TTsWNHl1yoyopthoSEaP78+YZljnpvAkBWyr2XUAG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      "text/plain": [
       "<Figure size 1200x600 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot them along with the real data set in random order subplot\n",
    "fig, axes = plt.subplots(5, 2, sharex=True, sharey=True, figsize=(12, 6))\n",
    "order = np.random.permutation(10)\n",
    "for order_i, ax in zip(order, axes.flat):\n",
    "    ax.hist(\n",
    "        replicates[order_i] if order_i < 9 else y,\n",
    "        np.arange(-45, 55, 5)\n",
    "    )\n",
    "    ax.set_yticks([])\n",
    "axes[0, 0].set_xlim([-50, 58])\n",
    "fig.suptitle(\n",
    "    \"Light speed example: Observed data + Replicated datasets.\\n\"\n",
    "    \"Can you spot which one is the observed data?\"\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compare the minimum of the real data set into the minimum of a replicated dataset.\n",
    "\n",
    "The distribution of the minimum value of a replicated data set can be \n",
    "calculated analytically. Consider $n$ samples of $X_i$, where $X_i$ has cumulative distribution function $F(x)$ and probability distribution function $f(x)$. The cumulative distribution function of the minimum of the $n$ samples is $1 - (1 - F(x))^n$ and the probability distribution function is its derivative $n f(x) (1 - F(x))^{n-1}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Calculate the pdf of the minimum of a replicated dataset\n",
    "x = np.linspace(-60, 20, 150)\n",
    "pdf = dist.pdf(x)\n",
    "cdf = dist.cdf(x)\n",
    "pdf_min = n * pdf * (1 - cdf)**(n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(figsize=(7, 4))\n",
    "ax.plot(x, pdf_min, '-', lw=2)\n",
    "ax.axvline(y.min(), color='C2', ls='--', lw=2)\n",
    "\n",
    "ax.set(xlabel='x', ylabel='p(x)', yticks=[], ylim=0)\n",
    "ax.set_title(\"Posterior predictive density for the minimum of a replicated dataset\");\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
